Best Known (94, 94+23, s)-Nets in Base 16
(94, 94+23, 95342)-Net over F16 — Constructive and digital
Digital (94, 117, 95342)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (83, 106, 95325)-net over F16, using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- digital (0, 11, 17)-net over F16, using
(94, 94+23, 1529304)-Net over F16 — Digital
Digital (94, 117, 1529304)-net over F16, using
(94, 94+23, large)-Net in Base 16 — Upper bound on s
There is no (94, 117, large)-net in base 16, because
- 21 times m-reduction [i] would yield (94, 96, large)-net in base 16, but